"Only by amending the constitution can we guarantee true democracy in our land," the Nobel Peace Prize laureate told her National League for Democracy (NLD) party at its Yangon headquarters.
The 2008 charter, passed by a referendum when Myanmar was still under military rule, cemented military control over the country's legislative body by making 25% of the members of parliament military appointees.
Aung San Suu Kyi said the army was "essential" in amending the charter, which is currently being debated by a parliamentary panel that includes soldiers.
"The tatmadaw (military) must not remain in a dilemma about whether to take part in amending the constitution. It must take part in it," she said.
President Thein Sein, a former general who has won international praise for reforms since he took power in 2011, on Thursday lent his support to constitutional reform in a monthly speech published in state media.
He also said he supported amending provisions which exclude anyone whose spouse or children are overseas citizens from becoming president - a clause widely believed to be targeted at Suu Kyi.
"I would not want restrictions being imposed on the right of any citizen to become the leader of the country," Thein Sein said.
The charter bars anyone whose spouse or children are foreign nationals or "owe allegiance to a foreign power" from being a presidential candidate. Suu Kyi has two British sons from her marriage to the late English academic Michael Aris.
As Suu Kyi arrived for her speech marking the 66th anniversary of Myanmar's Independence Day, NLD supporters chanted, "Aung San Suu Kyi for president," when the Nobel Peace Prize laureate arrived. The former British colony has scheduled a general election in 2015.
A day before Saturday's Independence Day, Myanmar freed about 2,000 inmates, including at least three political prisoners in a presidential amnesty.
Freeing political prisoners was one of the demands of Western democracies for lifting economic sanctions on the once-pariah state. Reform-minded President Thein Sein has released about 2,000 political prisoners since coming to power in March 2011.
Most sanctions have already been dropped on Myanmar, which was under military rule from 1962 to 2010.